arXiv research

The paper extends knot algebra with signs for more complex computations.

Method computes centers of Poisson and skein algebras for loops on surfaces.

New algebra pong algebra computed for knot Floer homology.

Generators and relations for knot Floer homology algebras computed.

New abelian quotient found in symplectic derivation Lie algebra.

New method uses algebras to speed up link Floer homology calculations.

Functional AD for Weil algebra computations.

Computes the component group of arbitrary real algebraic groups.

LightOn OPUs accelerate randomized numerical linear algebra, reducing computational costs.

Computes algebraic hull of Kontsevich-Zorich cocycle.

Cohomology of 'book' Lie algebra Poisson structure computed.

Non-associtive algebras is a research direction gaining much attention these days. New developments show that associative algebras and some not-associative structures can be unified at the level of Yang-Baxter structures. In this paper, we present a unification for associative algebras, Jordan algebras and Lie algebras…

New method computes automorphisms of surface groups using skein algebras.

We compute some value of the harmonic volume for the Fermat sextic. Using this computation, we prove that some special algebraic cycle in the Jacobian variety of the Fermat sextic is not algebraically equivalent to zero.

Computes cohomology of Steenrod algebra for k ≤ 5.

Improves an existing algorithm for computing algebraic set homology groups.

CoLA automates efficient numerical linear algebra for complex matrix structures.

New algorithm determines dimensions of hit spaces in polynomial algebra.

We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition. From a high-level perspective, the…

We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from describing these results, we discuss briefly the background as well as the importanc…

Compute central extension of mapping class group from stated skein algebra

Geometric AD framework simplifies derivative computation in JAX.

Develops a SageMath framework for computing characteristic classes.

Constructive approach to Lie algebra gradings, computing maximal and enumerating all gradings.

In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold ($C^{\infty}$ or complex analytic).

This paper presents algebraic structures of Lie-Butcher series.

Revives Vogel's diagrammatic technique for universal Lie algebra computations.

The exterior algebra of a vector space admits a family of braided Hopf structures.

Generalizes group cohomology and holonomy Lie algebra computations.

Simple construction of Rumin algebra for contact manifolds.

A new algebraic method for computing helicity is developed, by discovering a relationship between helicity of fluid mechanics and algebraic polynomial invariants of knot theory. We have constructed a topological invariant $t^{H\left(\mathcal{L}\right)}$ for a link $\mathcal{L}$ of knots, where $H$ is the helicity of a …

The main topic of this paper is two folds. First, we compute the first relative cohomology group of the Lie algebra of smooth vector fields on the projective line, Vect(RP^1), with coefficients in the space of bilinear differential operators that act on tensor densities, D_{λ, ν;μ}, vanishing on the Lie algebra sl(2,R)…

We introduce a bicomplex which computes the triple cohomology of Lie--Rinehart algebras. We prove that the triple cohomology is isomorphic to the Rinehart cohomology \cite{Ri} provided the Lie--Rinehart algebra is projective over the corresponding commutative algebra. As an application we construct a canonical class in…

In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R^3 of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute Groebner Bases and also on the memory capacity of the computer used to do the com…

We use computer algebra to demonstrate the existence of a multilinear polynomial identity of degree 8 satisfied by the bilinear operation in every Lie-Yamaguti algebra. This identity is a consequence of the defining identities for Lie-Yamaguti algebras, but is not a consequence of anticommutativity. We give an explicit…

Paper defines and computes a new weight system for gl_N Lie algebra.

Computes Lie algebra structure constants using a graphical calculus.

In GT/0006019 oriented quantum algebras were motivated and introduced in a natural categorical setting. Invariants of knots and links can be computed from oriented quantum algebras, and this includes the Reshetikhin-Turaev theory for Ribbon Hopf algebras. Here we continue the study of oriented quantum algebras from a m…

Lecture notes on using randomness in linear algebra.

A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…

Researchers compute c-projective symmetry algebras for Kähler surfaces.

Let $M$ be a compact oriented $d$-dimensional smooth manifold. Chas and Sullivan have defined a structure of Batalin-Vilkovisky algebra on $\mathbb{H}_*(LM)$. Extending work of Cohen, Jones and Yan, we compute this Batalin-Vilkovisky algebra structure when $M$ is a sphere $S^d$, $d\geq 1$. In particular, we show that $…

Let K be a compact Lie group. We compute the abelianization of the Lie algebra of equivariant vector fields on a smooth K-manifold X. We also compute the abelianization of the Lie algebra of strata preserving smooth vector fields on the quotient X/K.

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C^9 by employing differential algebra computer tools -- mostly within the Maple package DifferentialAlgebra -- in order to automate the handling of the arising h…

Machine learning accelerates Lie algebra computations.

Let $Γ$ be a finite group acting linearly on a vector space $V$. We compute the Lie algebra cohomology of the Lie algebra of $Γ$-invariant formal vector fields on $V$. We use this computation to define characteristic classes for foliations on orbifolds.

Algorithm simplifies computing knot invariants for weaving knots.

In this study, we classify some soliton nilpotent Lie algebras and possible candidates in dimension 8 and 9 up to isomorphy. We focus on 1 < 2 < ::: < n type of derivations where n is the dimension of the Lie algebras. We present algorithms to generate possible algebra structures.